This invention relates to a measurement method for thermal conductivity under steady state conditions at high temperatures which can be appropriately applied to various kinds of materials such as heat insulating materials.
In general, the thermal conductivity of insulating materials varies depending on the temperature. As shown in FIG. 14, it is a general characteristic that the higher the temperature, the higher the heat conductivity. In other words, heat is more easily conducted through a material at a high temperature than at a lower temperature. For heat insulating materials to be used at over 1,000.degree. C., it is necessary to test them at the temperatures at which they will be used.
A conventional method for measurement of thermal conductivity is described in ASTM C177-85 etc., for example, as shown in FIG. 15. A conventional apparatus for measuring thermal conductivity consists of a main heater b and an auxiliary heater c which are disposed respectively in the upper and lower parts of the enclosure a and are designed to generate a downward steady heat flow. A heat flow meter d is disposed above the auxiliary heater c and is used to measure the steady heat flow.
When thermal conductivity is measured with this conventional apparatus, a specimen S is first placed at the center of the enclosure a, and standard heat transfer plates S1 and S2 of known thermal conductivity are positioned on and under the specimen S. Second, the main heater b and the auxiliary heater c are controlled to create a steady state heat flow in the enclosure. The average temperature of specimen S is maintained at the temperature T.degree. C. at which the heat conductivity is to be measured whereas the temperature within the specimen varies as shown in FIG. 15.
Next, the steady state temperatures of the upper and lower surfaces of the specimen S are accurately measured with thermometers e. The thermal conductivity of the specimen S at temperature T.degree. C. (the average temperature of specimen S) can then be calculated from the temperature difference between the upper and lower surfaces of the specimen S and the value of the steady state heat flow which is measured by a heat flow meter d.
The following equation relates the heat flow Q (Kcal/h) at a state where the temperatures at the upper and lower surfaces of specimen S are, .theta..sub.1 and .theta..sub.2 respectively, the EQU Q=(.lambda./.tau.).multidot.A(.theta..sub.1-.theta.2)
From this formula, the following equation can be obtained: EQU .lambda.=Q.multidot..tau./A(.theta..sub.1-.theta.2) (1)
The standard heat transfer plates S1 and S2 in the above mentioned conventional thermal conductivity measurement apparatus are designed to keep the specimen S at a high temperature as well as to compare the thermal conductivity of the specimen with the known thermal conductivity of the standard heat transfer plates S1 and S2. This thermal conductivity can be obtained from the surface temperatures which are measured by thermometers f, and heat flow Q.
Heaters g for compensating the temperature of the inner surface of the enclosure `a` maintain the surface temperature as shown by the line B in FIG. 15. Thus, the heat transfer between enclosure `a` and its internal space is suppressed. This arrangement is for the purpose of preventing the heat flow through the peripheral part of the enclosure.
It is rather difficult or impossible at higher temperatures to conduct accurate measurement of thermal conductivity of a specimen with the conventional measuring apparatus since its surfaces are in contact with the standard heat transfer plates and thermocouples are used for temperature measuring. This limits the temperature at which the apparatus can be used.
It is possible to remove the upper standard heat transfer plate, but the lower standard heat transfer plate cannot be removed because the plate is indispensable in keeping the heat flow meter d at a lower temperature when the measuring temperature is very high.
In the above mentioned case, the upper surface temperature .theta..sub.1 of specimen S should be set slightly higher than measuring temperature T and the lower surface temperature .theta..sub.2 should be set slightly lower than temperature T. The mean temperature of .theta..sub.1 and .theta..sub.2 is then considered to be the average internal temperature of specimen S and can be regarded as the measuring temperature T at which the measuring will be conducted. In other words, the values of .theta..sub.1 and .theta..sub.2 are each kept at a point which satisfies the following formula. EQU T=(.theta..sub.1+.theta.2)/2
The assumption that mean temperature of the upper and lower surfaces is the internal mean temperature of specimen S is valid as long as the thermal conductivity of specimen S is constant and its internal temperature changes rectilinearly between .theta..sub.1 and .theta..sub.2 as shown as B in FIG. 15.
However, in reality, the thermal conductivity of specimen S varies according to temperature. Therefore the internal temperature does not change rectilinearly, but makes a curvilinear change shown as "B'" in FIG. 16.
For large temperature differences between .theta..sub.1 and .theta..sub.2 there is a big difference between the internal mean temperature T, obtained by assuming the simple average of .theta..sub.1 and .theta..sub.2, and the actual internal mean temperature T. Thus the simple average temperature of the two surfaces does not represent the overall mean temperature of specimen S.
However, if the temperature difference between .theta..sub.1 and .theta..sub.2 is small, the change of temperature can be regarded as a rectilinear change and the difference between the two values of temperatures T and T' can be disregarded.
However, if the temperature difference is too small, other problems will arise. Decreasing the amount of temperature difference makes it necessary to reduce the thickness of specimen S. The decrease in temperature difference however makes it more difficult to maintain the temperature difference between the upper and lower surfaces of specimen S constant. Furthermore, temperature measurement errors will cause a magnification of the error in the results, when the temperature difference is very small. For these reasons, it is virtually always the case that a large temperature difference is employed according to the conventional thermal conductivity measuring apparatus.